Exploring Adding and Subtracting Rational Expressions

This video tutorial explains how to add and subtract numbers in scientific notation. It covers the importance of having the same exponent for addition and subtraction, and provides multiple examples to illustrate the process. The tutorial also includes application and word problems to demonstrate real-world uses of scientific notation. The video concludes with a summary of how adding and subtracting differ from multiplying and dividing in scientific notation.

Why is it necessary to have the same exponent when adding or subtracting numbers in scientific notation?

• To avoid decimal points

• To treat them as like terms

• To make the calculation easier

• To ensure the numbers are in proper form

What happens to the exponent when you move the decimal point to the left?

• It remains the same

• It increases by one

• It decreases by one

• It doubles

In the example 8 times 10^3 + 1/2 times 10^3, what is the result?

• 8.5 times 10^3

• 9 times 10^3

• 7.5 times 10^3

• 8 times 10^4

When subtracting 6 times 10^10 - 1.2 times 10^11, what is the first step?

• Add the exponents

• Move the decimal of 1.2 to the right

• Move the decimal of 6 to the left

• Subtract the exponents

What is the result of 6 times 10^10 - 1.2 times 10^11?

• 5.8 times 10^10

• 0.6 times 10^11

• Negative 0.6 times 10^11

• Negative 6 times 10^10

In the example 8.1 times 10^-1 - 0.4 times 10^-1, what is the result?

• 7.5 times 10^-1

• 8.1 times 10^-2

• 8.5 times 10^-1

• 7.7 times 10^-1

How do you handle different exponents when adding or subtracting in scientific notation?

• Subtract the exponents

• Change the larger exponent to match the smaller one

• Change the smaller exponent to match the larger one

• Add the exponents together

What was the national debt in 2013 if it was 1.8 times 10^13 dollars and grew by 3.3 times 10^11 dollars?

• 1.83 times 10^12 dollars

• 1.5 times 10^13 dollars

• 2.1 times 10^13 dollars

• 1.833 times 10^13 dollars

How much closer is Jupiter to the Sun compared to Neptune if Jupiter is 4.84 times 10^8 miles and Neptune is 2.8 times 10^9 miles away?

• 2.316 times 10^8 miles

• 2.316 times 10^9 miles

• 4.84 times 10^8 miles

• 2.8 times 10^9 miles

What is the key difference between adding/subtracting and multiplying/dividing numbers in scientific notation?

• Multiplying/dividing changes the base

• Adding/subtracting changes the exponent

• Multiplying/dividing requires the same exponent

• Adding/subtracting requires the same exponent